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A mixed multiscale finite element method for elliptic problems with oscillating coefficients. (English) Zbl 1017.65088
This paper is motivated by the numerical simulation of flow transport in highly heterogeneous porous media. By using the most elaborated tools of mathematical finite element methods, the authors analyze a mixed multiscale finite element method with an over-sampling technique which is very well suited for solving second-order elliptic equations with rapidly oscillating coefficients. The multiscale finite element bases are constructed by locally solving Neumann boundary value problems. By assuming that the oscillating coefficients are locally periodic and by using homogenization techniques, the authors prove the convergence of the method. Finally, they report some numerical experiments which demonstrate the efficiency and accuracy of the proposed method. This paper is nicely written and looks like a strong mathematical and. numerical contribution to the subject.

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35B27Homogenization; equations in media with periodic structure (PDE)
35J25Second order elliptic equations, boundary value problems
65N12Stability and convergence of numerical methods (BVP of PDE)
76M10Finite element methods (fluid mechanics)
76M50Homogenization (fluid mechanics)
76S05Flows in porous media; filtration; seepage
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